City won the Premier League title last season while United failed to qualify from their group in the Champions League.
"We have to do better," Anderson told the club's official website. "Manchester United have to win every trophy and we're disappointed if we don't.
"There's always pressure to do well when you play for this club. Last season we lost the league on goal difference and everybody was sad. But we have to forget that and concentrate on this season."
He added: "I think the team looks good. At the beginning of the season it's always difficult but we've got a couple of wins and now we want more.
"Shinji Kagawa and Robin van Persie have a lot of quality. They make it easier for the rest of the team when they have so much talent.
"It also means everybody works harder to try and keep their own place."